TW201212140A - Advanced Process Control system and method utilizing Virtual Metrology with Reliance Index and computer program product thereof - Google Patents

Abstract

An advanced process control (APC) system, an APC method, and a computer program product, which, when executed, performs an APC method are provided for incorporating virtual metrology (VM) into APC. The present inventions uses a reliance index (RI) and a global similarity index (GSI) to adjust at least one controller gain of a run-to-run (R2R) controller when the VM value of a workpiece is adopted to replace the actual measurement value of the workpiece. The RI is used for gauging the reliability of the VM value, and the GSI is used for assessing the degree of similarity between the set of process data for generating the VM value and all the sets of historical process data used for building the conjecturing model.

Description

201212140 VI. INSTRUCTIONS: [RELATED APPLICATIONS] This application claims priority to U.S. Patent Provisional Application No. 61/369,761, which is incorporated herein by reference. The entire contents of the above application are incorporated herein by reference. [Incorporated by Reference] [Technical Field of the Invention] The present invention relates to an Advanced Process Control (APC) system and method, and in particular An APC system and method using virtual measurement (virtuai Metrology; VM) with confidence index (Reliance Index; ri). [Prior Art] Batch-to-Run (R2R) advanced process control has been widely used in semiconductor and TFT-LCD plants to improve process throughput. As defined by the SEMI E133 specification, R2R control is a technique for modifying recipe parameters; or selecting control parameters between batches to improve processing performance. A (process) batch can be a batch, a lot or a workpiece. When a batch is a batch, the R2R APC becomes a batch. To the APC of L(t〇-to-Lot; L2L); when a batch is a workpiece, the advanced process control of this R2R becomes a workpiece-to-workpiece (W2W) advanced process control . This workpiece can be a wafer for the semiconductor industry or a glass substrate for the TFT-LCD industry. L2L's first-pass control is now widely used to cope with advanced technologies. In the application of batch 201212140 cargo-to-Lot (L2L) control, it is only necessary to measure a single workpiece in the entire batch as the purpose of feedback and feedforward control. However, as component sizes shrink further, more stringent process control is required.

In this case, the control of L2L may not be accurate enough, and the control of W2W must be used. In the control of W2W, each workpiece in the batch must be measured. In order to measure each of the workpieces, the user has to use a large number of measuring tools and a significantly increased production cycle time. In addition, when the actual measurement of the workpiece is performed, measurement delays are inevitably caused, and this measurement delay causes complicated control problems and degrades the performance of advanced process control. To solve the above problem, a virtual measurement (VM) is proposed. Virtual Measurement System A technique that uses an estimation model to predict the measured value of a workpiece based on information about the process status of each workpiece. If the VM estimation model is sufficiently fresh and accurate, then it can generate a virtual measurement (VM) value within seconds of collecting the complete machine process data for a workpiece. Therefore, this VM value can be applied to W2W control. Please refer to FIG. 1 , which is a schematic block diagram of a conventional model of Exponentially Weighted Moving Average ( EWMA ) R2R control, which is disclosed by a paper proposed by M.-F. Wu et al. "Performance Analysis of EWMA Controllers

Subject to Metrology Delay55, M.-F. Wu, C.-H. Lin, DS-H. Wong, S.-S. Jang, and S.-T. Tseng, published in IEEE Transactions on Semiconductor Manufacturing, vol. 21, no. 3, pp. 413-425, August 2008), this paper is incorporated herein by reference. First, consider a process model with linear input and output relationships: 201212140 where a is the output of the production machine; % is the control action taken by the process batch; is the initial bias of the process (Initial Bias); Gain; and the % DisturbanceM〇del input. A process prediction model is known, in which the tether is for a system-estimated gain parameter (e.g., chemical mechanical polishing (CMP) removal rate) and its initial value can be obtained from the actual machine/recipe performance. (2) When using the EWMA filter, the model offset or disturbance of the &+7 process batch can be estimated as f1k+{=a{yk-Auk) + {\-a^k where α is EWMA coefficient between 0 and 1. The female +i process batch control action is (3)

u Tgt-ή^ k+l A where the term represents the target value. Please refer to FIG. 2, which is a block diagram showing the conventional W2W control mechanism using virtual measurement, wherein the actual measured value of the sampled workpiece of the zth process batch measured by the measuring machine 20 is used; The virtual measurement value of the first process batch of the system; and the process parameter data of the process machine 10 of the A-stage process batch. In the paper shown below: "On the Quality of Virtual Metrology Data for Use in the feedback Process Control", AA Khan, JR Moyne, and DM Tilbury, published in Proc. AEC/APC Symposium XIX - North America, Palm Springs , CA. USA, Sep. 2007; “An Approach for Factory-Wide Control Utilizing 201212140

Virtual Metrology", AA Khan, JR Moyne, and DM Tilbury, published in IEEE Transactions on Semiconductor Manufacturing, vol. 20, no. 4, pp. 364-375, November 2007; and "Virtual Metrology and Feedback Control for Semiconductor Manufacturing Process Using Recursive Partial Least Squares 55, AA Khan, JR Moyne, and DM Tilbury, published in Journal of Process Control, vol. 18, pp. 961-974, 2008, these papers are incorporated herein by reference, Khan et al. The controller 40 proposes to modify the above equation (2) as follows: When the system is measured by the actual measuring machine 20, it becomes a normal, and uses the EWMA coefficient % in the following equation (4): 7*+ι = a \{y. ~ ^uk) + (1_a\)Vk (4) When the eight systems are estimated or predicted by the virtual measurement module 30, they become Λ and use the EWMA coefficient α2 in the following equation (5) Medium: %+1 = α2(Α-办*) + (1 - "2)4 (5)

Khan et al. pointed out that % > α2 (usually depending on the quality of the virtual measurement data). At this point, the problem of applying the controller gain of the virtual measurement is to focus on how to set α2, where the basic principle is that α2 should be based on the quality of the virtual measurement data, and % < % ). Khan et al. proposed two virtual metrology metrics (Metrics) to consider incorporating the quality of the measurement data into the controller gain of the R2R controller 40: 1. The prediction error of the measurement batch: Error = -j) ( 6) 2. If 7 and $ are zero-mean Gaussian Deviations with a mean value of the target value, Bayi 1J is based on the minimum mean square error estimate of y (Min mean-square-error (MSE) ) estimator) is: 201212140 (7) where the correlation coefficient is: pc〇vb,j)] (8) and 5 and σ are the standard deviations of _y and 3> respectively. However, the two measures proposed above have the following disadvantages: 1. Equations (6) and (7) require actual measurement data to be “less”; however, if a continuous measurement data (actual measurement value) is available, then it is not necessary at all. Virtual measurement (j)); 2. Because of the value of p; ^ can be positive or negative, so u can not be normalized to between 0 and 1. For the above reasons, the prior art cannot easily combine the data quality measurement as shown in equations and (7) into the R2R controller. [Summary of the Invention] It is to provide an advanced process control /, in order to effectively take the virtual measurement data quality into the R2R controller, to the virtual amount of the reliable ^ 22 control in the yoke Test back to X to make the _process (four) performance upgrade. According to one aspect of the present invention, the measuring machine, the ^^ιj, the system includes the processing machine, the quantity/J-micro port I, the analog measuring module, the confidence indexing machine ##用桐秘★ &amp ; ^ Ting group and R2R controller. The process machine core system processes the historical workpiece according to the complex array history, and processes a plurality of process batches according to the complex array material:; The measuring material is used to measure a plurality of workpieces into a J-port for measuring historical workpieces and a plurality of sampled workpieces selected from the above-mentioned workpieces of 201212140 to provide a plurality of historical quantities of historical workpieces and have been processed in the process batches. The actual measured values of the sampled guards. The virtual quantity measurement module (4) is used to provide a plurality of virtual measurement values of the system by inputting the group process parameter data to the estimation model, wherein the estimation model is based on the estimation algorithm. The historical process parameter data and the historical measurement value are used, wherein the historical measurement value is the measured value of the historical security member manufactured according to the historical process parameter data. The signal module is used to generate a plurality of process batches: index values (Reliance Index; and /), each of which corresponds to the heart value of the process batch is calculated by calculating the virtual M quantity of the workpiece. Statistical distribution: (Statistics Distribution) is generated by the overlapping area between the statistical distribution of the reference prediction values of the workpiece, wherein the reference prediction value of the workpiece is generated by using the process parameter data of the workpiece into a reference model, and The establishment is based on a reference algorithm and uses the historical system Z-mode to correspond to the historical process parameter data one-to-one history # data and the estimation algorithm and the reference algorithm must be different algorithms. = The larger the area, the higher the confidence indicator value, representing the correspondence to confidence: and the higher the credibility of the virtual measurement. The R2R controller is a system that does not have a value to control the process to make a batch of the process:, the following off w*+i _ 茗 (G2, i, G2, 2, ..., G2, y, nine), G2, , = / W) xGm ; where if private < call, then 〇 2 〇, or use & not batch to batch controller; Weekly and if MC 'th/(/%) = % ; 201212140 If RlkkRJT ΜΛ>(〇' then 八叫=1_队., - 2 of them represent samples that have been processed in the second process batch The measured value of the workpiece, Wz+1 represents the control action of the ζ+/th process batch when less Ζ is used; Gu• represents the controller gain applied to the R2R controller when using 凡 (Gain ), where z• represents the number of controller gains applied to the R2R controller, and for a long time represents the virtual measurement of the workpiece that has been processed in the A-process batch; w correction represents the use of a long time moxibustion +7 process batch control actions; Gy represents the controller gain applied to the R2R controller when pill is used, and /t represents the confidence indicator value for the & process batch; and 4 represents a maximum based on One of the upper limit of the allowable error and the /th threshold, which is defined by the error of the virtual measurement obtained from the estimation model; and C represents the number of a predetermined process batch. In one embodiment, the foregoing APC system further includes an overall similarity indicator module for Enter the process parameter data into a statistical distance model to provide a plurality of overall similarity index values (G1〇bal Similarity Index; G57). The statistical distance model is based on a statistical distance algorithm and uses historical processes. Parameter data, if it is (3⁄4 yield 0' or adopt 9_, instead of adjusting the R2R controller for a long time, where (73⁄4 represents the overall similarity index value of the first process batch; GS/r represents the threshold based on one) The G57 threshold is defined as 2 to 3 times the maximum GS/value of the historical process parameter data. According to still another aspect of the present invention, in an advanced process control (APC) method, a step is performed to obtain a complex number Group history process parameter data, wherein the group history process parameter data is used by a process machine to process a plurality of historical workpieces. A further step is performed to obtain a historical workpiece that is measured by a quantity measurement 201212140 machine : (4) The process of estimating the estimator and the historical process parameter data-2 to estimate the model, and based on the algorithm to establish a reference model, in which The algorithm used in the interpretation of the burdock spring must be different. The implementation of the H secret one == enough to control the aforementioned process machine according to the above relationship to the distance t real towel, the aforementioned APC method further includes: according to a statistic = away ^法和^Historical process parameter data to establish - statistical distance model to ^ the R2 R controller can be controlled according to the following relationship control = process machine to process batch batch '若卿> view, then, production 0, used instead of long to adjust the R2R controller, its towel represents the overall similarity index value of the moxibustion-human process batch; G57r represents a (7*S/threshold value, the definition of this gamma threshold is history Maximum processing parameter data: 2 to 3 times the similarity index value. According to still another aspect of the present invention, a computer program product is provided. When the brain is loaded into the computer program product and executed, the APC method can be completed 0 times. Therefore, the embodiment of the present invention can be effectively applied. The virtual quality measurement index is considered to be the jump control H towel, so as to overcome the reliability problem in the virtual measurement feedback loop that cannot be considered 2R control, = advanced process control performance upgrade.实施 Embodiments Referring in detail to the embodiments of the present invention, examples thereof are described in conjunction with the drawings 201212140. Wherever possible, the same reference numerals are used in the drawings to refer to the same or similar components. Referring to Figure 3A, there is shown a schematic diagram of a W2W APC system in accordance with an embodiment of the present invention. The Apc system of this embodiment includes: a processing machine 100, a measuring machine 110, a virtual measuring (VM) module 12, a confidence indicator (RI) module 122, and an overall similarity index (Gsi) module. And R2R controller 130. The process machine 1 is operated to process a plurality of historical workpieces according to the complex array history process parameter data, and is operable to perform a plurality of process batches for the plurality of workpieces according to the complex array process parameter data. A process batch is a unit controlled by the R2R controller 130, wherein when a process batch is a batch (Lot), the R2R controller 130 is an L2L controller, which is controlled by a batch of goods. The process machine 1〇〇; when a process batch is a workpiece, the R2R controller 130 is a W2W controller, which controls the process machine 1 by one workpiece and one workpiece. Typically, a lot of goods consists of a plurality of workpieces, for example: 25 workpieces, meaning that the L2L controller controls a process batch to process 25 workpieces with a set of process parameters. The measuring machine 110 is operated to measure historical workpieces and a plurality of sampled workpieces selected from historical workpieces to provide a plurality of historical measurements of historical artifacts and a plurality of sampled workpieces that have been processed in the process batches. Actual measured value. The virtual measurement module 120, the confidence indicator module 122, and the overall similarity indicator module 124' must first establish an estimation model, a reference model, and a statistical distance model. The estimation model is established according to a calculation algorithm and uses historical process parameter data and historical measurement values. The historical measurement value is based on the actual workpiece of the historical workpiece corresponding to the historical process parameter data. 2012 12140 The measurement model is based on a reference algorithm and uses historical process parameter data and corresponding historical measurements; the statistical distance model is based on a statistical distance algorithm and uses historical process parameter data. The estimation algorithm and reference algorithm can be Multi-Regression (MR) algorithm, Support-Vector-Regression (SVR) algorithm, Neural-Networks (NN) algorithm. Partial-Least-Squares Regression (PLSR) algorithm or Gaussian-process-regression (GPR) algorithm. The statistical distance algorithm can be a Mahalanobis Distance algorithm or an Euclidean-Distance algorithm. The algorithms described above are for illustrative purposes only, and other algorithms are of course also applicable to the present invention. The RI and GSI used in the embodiments of the present invention can be referred to the U.S. Patent No. 7,593,912, the entire disclosure of which is incorporated herein by reference. The RI model, the GSI, and the VM model used in the embodiments of the present invention can be referred to the U.S. Patent No. 7,603,328 and U.S. Patent Publication No. 20090292386, the disclosure of which is incorporated herein by reference. It is worth mentioning that the same assignee as in this case is disclosed in U.S. Patent No. 7,593,912, U.S. Patent No. 7,603,328, and U.S. Patent Publication No. 20090292386. The virtual measurement module 120 is configured to provide a virtual measurement value of the process batch by inputting the process parameter data to the estimation wedge type. Confidence indicator module 1 is used to generate the virtual measurement confidence indicator value of the process batch (and, each confidence indicator value corresponding to the process batch is calculated by calculating the virtual measurement value of the workpiece and the workpiece The reference area between the statistical distribution of the predicted values is generated, wherein the reference prediction value of the workpiece is input by the workpiece 13 201212140

· τ 日 Your value is the higher the credibility of the measured value. Based on a maximum allowable error J, in this embodiment, the / threshold value (like 9 system > test algorithm may be different. When the aforementioned overlapping area 1 曰 your value is high, representing the value corresponding to the confidence index The upper limit of the maximum allowable error is defined by the error of the virtual measurement obtained from the estimation model. The overall phase 5 indicator module 124 is used to input the process parameter data to the statistical distance type. 'To provide a plurality of overall similarity index values for the process batch (Q) is to evaluate the similarity between any new process data and all process data (historical process parameter data). In this example: The representative is based on a threshold value, which is defined as 2 to 3 times the maximum G57 value of the historical process parameter data. The following 'for convenience of explanation' R2R controller 130 is exemplified as an EWMA controller. However, the R2R controller 130 It can also be a moving average (ΜΑ) controller, an exponent weighted moving average (EWMA) controller, a double exponential weighted moving average (0〇111) 16£墀]\4人;(1-£\¥]\4 8) Controller, or a Proportional-Integral-Derivative (PID) controller. Please refer to Figure 3B, Figure 3B shows A schematic diagram of an EWMA controller in accordance with an embodiment of the present invention. The present invention is characterized by overcoming the controller gain problem of how to set the EWMA coefficient α2 of equation (5) for application virtual measurement, wherein the basic principle is α2 It should be determined according to the quality of the virtual measurement data, and the embodiment of the present invention uses G57 201212140 to estimate the quality or reliability of the virtual measurement value. The numerical value is an excellent virtual i measurement evaluation index and 0 < Along the < 1, the higher representation represents better than the virtual measurement reliability, so the EWMA coefficient α2 can be naturally set as follows: a2 = RIxal (9) where the EWMA coefficient % is the same as equation (2) Equation (9) is applied when the R2R controller 130 requires a relatively high gain. The condition that requires high controller gain is that it is relatively unstable from the target value or the production process. Conversely, if eight is close to the target value Or production process relative For stability, the controller gain should be taken as a small value. To generate a smaller controller gain value, the EWMA coefficient seven can also be set as follows: a2 = (l-Rl)xai (10) Only if and / is good enough Equations (9) and (10) are valid. In other words, 'must be greater than 妳. If it is called, this virtual measurement cannot be used to adjust the R2R controller gain. In addition, because the system design is used to assist W to determine the virtual quantity. The reliability of the measured value, so when it is still 'the corresponding virtual measured value can not be used. The conclusion is that if 'should be < or GiS7> G*S7r, the inner is set to 〇. The following considerations are given to the R2R controller gain management issues in the actual production environment whenever the process machine 100 is being serviced or tuned. Usually the production process of the first batch (just after repair or adjustment) is relatively unstable, so the controller gain value should be relatively high. After the completion of the production process of the first batch, the production process will become more stable. In other words, the rest of the shipment should have a smaller controller gain value. - In summary, A can be set to: 15 201212140 a2=f(RI, GSI^a, (u)

• r 0, iiRI<RIToi· CrSI> GSIT

f(RI, GSI) = ^ RI? iiRI>RIT and GSI < GSITmd for k < C -\-RI, if RI>RIT and GSI < GSIT and f〇r /c > C (12) C Represents the number of preset process batches. Taking the W2W control of the semiconductor industry as an example, C can be 25. Since the R2R controller 130 can also be an MA controller, a dual-finger EWMA controller, or an HD controller, a general-purpose main control equation is provided as follows. (13) (14)

Wz+1 =容(Gl,丨,G 丨,2,".,GM, less J WA+1 =g(G2,l,G22,...,G2,,;pA) G2J=f(RIki GSIk)xGl. (15) Where if GS7>GS7r, then (}2 corpse, or use IX instead of λ to adjust the batch to batch controller; bitter RIk> RlT watt GSIksGSITmc, against Qing (4): Team RIkkRIT See GSIkSGSITXk>CjyUpGsiM — jUk where h represents the actual measured value of the sampled workpiece that has been processed in the zth process batch; Mz+1 represents the z+7th process batch when % is used The control action 'Gu represents the controller gain (Gain) applied to the R2R (4) when % is used. 'where z• represents the number of controller gains applied to the R2R controller'. The domain table is already in the under-process batch. The virtual quantity of the processed workpiece is the first (1) read batch of 16 201212140 control action; G2, which represents the application of λ to the r2 r controller controller gain (10) represents the A process offset Confidence indicator value; private, the table is based on the maximum value of the maximum regrettable upper limit, and the maximum allowable error upper limit depends on the virtual measurement value obtained from the deferred type The difference is defined; the representative is based on the -(10) gate value, which is defined as the maximum of the historical process parameter data (2 to 3 times the edge; and c represents the number of a preset process batch. MA controller And the EWMA controller is a single gain controller; the double exponentially weighted moving average controller and the PID controller are multiple gain controllers' which are described below. M_A controller η-terms MA controller's zth 7th batch Control action of "Run", "ζ+ι, is derived from

U 2+1 THi_ (16) where the money is estimated for the gain parameter of the system (eg chemical mechanical polishing removal rate), which is the target value of the z+7th batch, and the L system is the model of the z+7th batch Offset or disturbance. The z+7th batch-human model offset or disturbance of the n_term MA controller can be expressed as follows: = -(y,~Auz)+-(yz^Au) 1 n 1 w = «Σ(Λ - ήζ+, = -Ir,, ^ a.. \ , 1 / . , L... + 丄(Λ-("-ι)如1)

Au2) M\hMA{q){yz- Auz) 17 (17) 201212140 Its ^ represents the actual measured value of the Zth batch control output; g represents the delay operator, ie 疒, =Λ1; M 尸W Gain for the controller; and 08), (4) = (l + g-1 +... cut ten_1)) Next, available from equation (16)

U ζ+1 1&:

A SMA{^^yz) (19) The conclusion is that the control heart +1' of the z+7th batch of the η-item controller can be expressed as the actual measured value of the zth batch control output. With the controller gain, M;, the function. Meaning, EWMA # ^.[ s , the z+7 of the EWMA controller: The control of the run is represented as equation (16). Also for the EWMA controller, you can derive the heart +1 as follows: ^z+i = «ι{yz ~Auz) + {\~αχ)ήζ +♦Cake:-also)+·..cut 1(1— "Peak (1_αι^ =gαι(1 -αι广'Ο, ―,,), initial condition 々.=〇C0=«l 02=^(1-^)2 201212140 Then-(zl) ){yz- Auz) (21) : lc〇zV(z-1)_ (22) ~ ^ SEWh4Aiavyz) (23) ^z+i ~ (c〇+ c, · 1 η-----hc(. -q~ ' + —μ c 丨.< = αΑ_(αρ“)(凡-A) and lEWMAy The conclusion is the control action of the 2+7th batch of the EWMA controller, «ζ+1' can be expressed as the zth The function of the actual measured value gain % of the sub-batch control output. The control action of the z+/time batch of the d-EWMA controller for the d-EWMA(4)|] can be expressed

Uz+l=^izinz£^LA (24) Please refer to equations (2〇), (21) and (22), where 1 can be expressed as: ^ζ+ι = «1,1 (λ ~ ) + (1 - or,, )ήζ =a^hEfVMA(al l,q)(yz _ (25) Similarly, Λ+1 can be derived as: Λ+ι =ai2(y2-^z-^) + (\~al2 ) pz =CC^EWMA (^1,25^)(λ ~ Auz-η2) (26) The last 'wz+} can be expressed as: ai,2, less z) The conclusion is the d+EWMA controller's z+ / u , (27 batch control! Z+IA ~ ^d-EWMAK^iiy 201212140 κ can be expressed as the number of batch control and controller materials (four). ^ Actual measurement value π gID control 1 § The control action of the 2+th/sub-batch of the wide D controller can be expressed as: (28) = wn "o, again" Z+ / sub-lot control action, 仏 +1, the actual measured value The fork, and the controller conclude that the PID controller can be expressed as a function of the zth batch control output gain, especially Λ/和尤ΛΖ). Observing equations (19), (23), (27), and (28), the z+y human-human control action of the MA controller, EWMA controller, d_EWMA controller, and nD controller 'Wz+&quot ; can be expressed as a function of the actual measured value of the zth batch control output & and the controller gain Gii, Gi, 2..々%, where z• represents the number of gains present in the controller. ~=购,丨,G 丨y'GuJ (29) For the MA controller '戸1 and Gl l = slave; for the ewma controller ' /=1 and Gu=% ; for the d-EWMA controller For example, 戸2 and GM=au and GU2= au; for the PID controller, 戸3 and Gi,i = i^, gi,2 = 尺;, / and in fact, equation (29) is already in the equation Mentioned in (13). When virtual measurement is used, only the buffer is replaced, and the controller gain becomes Gy, G2, 2, ..., and G2)i· ' where / represents the number of 20 201212140 gains present in the controller. Therefore, by using virtual measurement, 帛...sub-lot control action, the general type of wz+1 is: (30) ^+1=^〇2ιΙ, ο2 25...>〇2,,^) For the controller, /=1 and G21 drink; for the EWMA controller and Lu Wei 1 and Gm; for the d_EWMA controller, 12 and G2 α and know: gas 2; for the PID controller, 13 And wide ', and G2, 3 hearts. In fact, the equation (3〇) has been mentioned in equation (14). ^ When the quasi-measurement is used as the R2R control (4), the controller gain can be adjusted using the Ik virtual 1 and / and GiS7 as follows: ^2, / = f{RI, GSI) XG, in fact, the equation (31) has been mentioned in equation (15). (31) Specifically, for the case of MA: (32) M2=fMA{RI, GSI)xMx For EWMA: (33) (34) (35) ~ Iewma GSI) X CKj For d-EWMA: A2,i=fai (8), GSI)xau 0^2,2 =fa2(^>GSI)xal2 For the case of PID: K2P=fp(RI,GSI)xKlp κ,^/^ιυ,ΟΞηχκ,,

^2, D = fD(RI, GSI)xK]D, and conclude that all Gu controller gains can be specified as constants or adjusted by the mechanism or function being adapted. When the actual measured value 匕) is used, 21 201212140 can be designed and specified G,,,. After specifying Glw., if the virtual measurement value is used (the magic is used instead of the time), the Gf can be designed and specified as shown in equations (31)-(35). • Equations (31)-(35) are only in the hole/and Only when G57 is good enough;

h ′ RI 簏 is greater than rjt^_ GSI vine, \, in GSIT. If ri&lt;rjt gas GSI &gt; GS7r' then its corresponding virtual measurement cannot be used to adjust the R2R controller gain. The conclusion is that if you follow </ br> or GS7&gt; GS/r, then the situation is .. § History = &amp;, that is, instead of long time to adjust the R2R controller; for EWMA: set or % = 〇 (ie G2/=〇); For dE WMA: set 1 and A+|=A; or set %"=^ 2 = 〇 (ie G2/=0); For PID: set +7 = call, ie Use a nine-i instead of a long time to adjust the R2R controller. The following describes the algorithm and its operation process. Confidence indicator an As shown in Table 1, it is assumed that the data of the group measurement is currently collected, including the process parameter data (υ=/, 2,··_, „) and its corresponding actual measured value data. , 2, ..., where each set of process data contains one parameter (from parameter to parameter p). In addition, (_) the process parameter data of the actual production process is collected, but there is no actual except for +1 The measured value data, that is, in the workpiece actually produced by the (m-η) pen, only the first workpiece is measured, for example, the actual measurement is performed, and then the actual measurement is performed by Λ +1 to infer the quality of the other parts. Information example 22 201212140

In Table 1, less, v in the production of the workpiece 1 2 flute 2 is the historical measurement, ~ is normal, - the actual measured value of the group. =] / the actual measured value of the solid workpiece. The standard deviation is . The force is the average number. The actual mean and the standard deviation will be all =, _))' where each - Z; the number 夂 mean = also 0 is the difference is V ·). For the actual measurement data, if the next reading is closer to the specification center value. Its standardization is 5 such as 7 _ yj~y % i = 1,2,···,η

(v/ + less 2+...+ less „) (36) (37) 23 201212140 °y=^~j{yi~y)2 +(y2-y)2 +---+(^-37)2 (38) where is less, is the actual measurement data of the group / group; &amp; is the actual measured value data after standardization of the /group data; V is the average of all actual measured data; 5 is all actual The standard deviation of the measured value data. The description here is based on the application of the neural network (NN) algorithm estimation algorithm to establish the estimation model for the virtual measurement, and the reference algorithm such as complex regression algorithm To establish a reference mode for verifying the estimation mode. However, the present invention may also use other algorithms as a estimation algorithm or a reference algorithm, as long as the reference algorithm is different from the estimation algorithm, such as a complex regression algorithm. , support vector machine algorithm, neural network algorithm, partial least squares algorithm or Gaussian program regression algorithm, so the invention is not limited to this. When applying neural network algorithm and complex regression algorithm, such as its convergence condition Under the condition that the Sum of Square Error (SSE) is the smallest, and the two modes are respectively The actual measured values after normalization are defined as AND, and they should all be the same as the actual measured actual values ^. In other words, when "+〇〇, = = represents the actual measured value after standardization, But change the name for the purpose of different modes. So V, ~ bucket ', σ! J, and ~~, eat), means ^ and hurricane. For the same assignment, but due to different estimation modes, make the two The average of the prediction algorithms is different from the estimated value of the standard deviation. That is, the average and the standard deviation estimation formula after the 201212140 conversion (&lt;^ will be averaged with the complex regression model) Estimation formula (Α 准 estimator (different eating. y' confidence index value is designed to judge the credibility of the virtual measurement value, so the confidence indicator value should be considered to the statistical distribution of the virtual measurement value % and actual measurement The statistical distribution of values ~ the degree of similarity between the two. = And, when applying virtual measurements, no actual measured values can be used to evaluate the imaginary, reliable value of the measured values (obviously, if obtained The actual measurement does not require virtual measurement. Therefore, the present invention uses a statistical distribution estimated by a reference algorithm (for example, a complex regression algorithm) to replace the statistical allocation. The reference algorithm of the present invention may also be other related prediction algorithms, so the present invention is not here. Referring to Figure 4, there is shown a schematic diagram illustrating the L% heartmark value of a preferred embodiment of the present invention. The confidence index value of the present invention is defined as a calculation, estimation mode (e.g., using a neural network ( NN) algorithm) prediction (virtual measurement) allocation 2 machine and reference mode (for example, the use of complex regression calculus (reference measurement) allocation between the intersection area coverage value (overlap area A ). Therefore, the formula for the confidence indicator value is as follows:

2

(39) where ^^ 2~ When &lt;2j&gt;Ni then 0 = 2^ σ is set to 1 25 201212140 k The heart index value increases as the overlap area A increases. This phenomenon indicates that the results obtained by using the estimation mode are closer to those obtained by using the reference mode, and thus the corresponding virtual measurement value is more reliable. Otherwise, the corresponding degree of the virtual measured value decreases as the overlap area A decreases: when 2 is the estimated allocation and the estimated allocation &amp; completely overlaps 'according to the statistical distribution theory The value of the confidence indicator is equal to i. And when the two distributions are almost completely divided, the letter 4 value is close to 〇. The following describes the estimation method to calculate the virtual measurement value 孝口 allocation method. In the estimation mode, if the convergence condition is to minimize the sum of the squared errors, the false a can be given to the given heart~, the distribution of z is = the gamma, ie, given, down, ^^ y丨, ~ ° Ten is '=2, the NN estimate of σ1 is 呤=矻. In the process of ΝΝ ΝΝ 的 的 的 々 々 々 ‘ data standardization steps. For the 4th construction, the process parameters must be processed first. The NN estimation mode process parameters (4) The standardization formula is as follows: zx . t ,, J aXj j = .p (40)

X; .+JC

(41) ~/ + (X2J-Xj)2+... + (xnj-3c.y) where (42) ~ is the y. turn parameter of Cheng Jin shot; % is the third set system The number of processes after the standard consumption is 26 201212140; ^ is the average of the 7th process parameter data; 'is the standard deviation of the y. process parameter data. Use this A7 group standardization process to standardize this A7 group After the actual measurement '枓 = with .··, 吣 = and then. Then, in person, ~^7,2,.., ") to construct &gt; ^ estimation model (Z ~,, = U ...,W&quot;=U ) to the virtual quantity after the NN spear king material is normalized, in order to obtain the corresponding standard yNi .·· , 2V &gt; γΛ , thus ' ~ (ie Α -ζ 〇 呌 〜 〜 ~ ..., ^. 41, ~ ~ _ Ζ ~) estimated leaf value and σ7 ..., the value can be calculated by the formula shown below:, (P estimate

Syi ~ΖρΝί, ί=^,2,··, η}η+Ι,··, m

(43) (44) (45) Z^=iSZh^ZyN2^^Zhn) where ^ is the average of the virtual measured values after normalization. : The following is a description of the basic prediction of the complex prediction algorithm by the complex regression model. The basic assumption of the complex regression algorithm is "the given number is equal to %, the distribution of the change", that is, given Ζ-~#k,,, 4). And the complex regression estimator is &gt;; the sub-gas = 3⁄4, and the complex regression of 呤 is the process data obtained after the standardization of the A7 group. k 27 201212140 The actual Jinding and Lili value of this /7 group standardization The relationship must be determined by the use of complex regression analysis, -(βββ β , ,, the weight corresponding to the two households is m'. The construction and relationship are as follows: ~+H//+久~+ . 2,P y2 0r〇+ fif.fZY +β 7 Ά\2+··.+ΑνΛ ”·ρ y&quot; 1,2 ' ' +PrpZx,=2' (46) Suppose Ζ, ,ζ , ( 47)

ζ yn Ί ·* 2 \ Λ1, 1 Z, · ;-P ·_ 2 Zx = 2.1 • · « xIp • · • · 1 A , · • 2 \ nj X n, PJ (48) Number === The least flat method of : can be obtained by reference fir=\2lXZ: ζ. Then, the complex regression mode can be obtained (49)

^γη ~ Κ〇+ β,· jZ

XU^K2ZX i,2+ ...+ is rpZx 1 &gt;2,...,n,n+1

, -.P 28 (50) 201212140 Therefore, in the estimation stage, after the process parameter data comes in, the corresponding complex regression estimate &amp; can be obtained according to the formula (5〇). The complex regression estimate of the standard variogram ^ - is for the heart: ' ^ h , %,

+izyr2~^py+---+{zyr„~^yy (51) (52) When the estimator of the NN estimation model is obtained, and the estimation formula of the complex regression model is used, it can be drawn as 4A. The normal distribution map shown in the figure 'calculates the prediction of the prediction (virtual measurement) using the estimation mode (for example, using a neural network (NN) algorithm) and the prediction of the reference mode (for example, using a complex regression algorithm) ( The reference area coverage value (overlap area A) between the assignments of the reference measurement values can be obtained for each one (the confidence value of the virtual measurement value is 0. The gate broadcast = fixed one - Γ, then the virtual measurement The reliability of the value is 3 and the following describes the method of determining the confidence indicator: - Before setting the confidence indicator (4), the upper limit (6) is required first. The error of the virtual measurement is the actual amount, the domain The difference between the ^ obtained by the estimation model 2 = the actual measurement (four) the average (10) absolute (four) percentage, that is, all 29 201212140

Error) y^-ym y :100% (53) Then, the maximum allowable error upper limit can be specified according to the error defined by equation (53) and the accuracy of the virtual measurement (five 〇. Therefore, the confidence threshold value (Defined as the confidence indicator value (and /) corresponding to the maximum allowable error upper bound (A), as shown in Figure 4B. That is, Γ = 〇 1 - Lu)! dx (Μ) // and σ Defined in equation (39); and ZCerMr=Z, NI+\yx{EL/2)]/ay (55) where % is defined in equation (38). The algorithm and its operation process are presented below. Overall similarity indicator When applying virtual measurement, there is no actual measurement available to verify the accuracy of the virtual measurement. Therefore, the confidence index value (and /) is calculated by substituting the normalized complex regression estimate &amp;, instead of the normalized actual measured value '. However, such substitution may result in an error in the confidence indicator value (/?/). To compensate for this situation, the present invention proposes an overall similarity indicator (GS7) of the process parameters to help determine the reliability of the virtual measurement. 30 201212140 The concept of OS7 proposed by the present invention is to compare the data of the process parameters of the input system of the test system with the data of the virtual quantity, and obtain the similarity degree of all the historical parameter data when the input process of the process is entered. index. The number of data and all historical reference inventions can be quantified using a variety of different statistical distance departure algorithms). The Markov distance ^ # method (for example, the Markov's distance from P.C. Mahalanobl introduced in 1936) is based on the correlation between variables to identify and analyze. This technical means is not 4 sample groups and known samples == method 'This method is related to the data group and has scale invariance

Invariant), ie not related to the magnitude of the measured value. If the data is similar, the calculated Mahalanobis distance will be smaller. The present invention utilizes the calculated magnitude of (10) (Machine distance) to distinguish whether the new process parameter data is similar to all of the modeled processes (4). If f is small, it means that the new process parameter data is similar to the process recipe of the model. Therefore, the virtual measurement value of the new process parameter data (high similarity) will be purely accurate. Conversely, if the calculated (10) is too large, the confidence of the new process parameter data and the modeling process “(4) μ = the accuracy of the virtual parameter of the process parameter data (low similarity) is low. Standardized process parameter data ^ (4.), (9) and ^ · / · Ζ ~ · ί, 々 ·., ρ. So, select: i: r 〇 rr ^ &quot; all parameters are 31 201212140 〇 Next, calculate the correlation coefficient between each standardized modeling parameter. ' Assume that the correlation coefficient between the sth parameter and the tth parameter is rst, and • where there is 1 more data, then I kj ~=ΙΓ7 ( Ζ&quot;· wz,2+...+Zsr~) (56) After completing the calculation of the correlation coefficient between the parameters, the correlation coefficient matrix can be obtained as follows: 1 rl2 ··· rIp R = (57) r2l 1 ·· · r2p • · · · · · · · ^pi ^p2 ...1 Assuming that the inverse matrix of λ (ir;) is defined as j, then a=r! all α2ι

. !2 ...p . 22 ...A p ap2 .· app (58) In this way, the second standardization process parameter data (the standard parameter data of the standardization (the Mahalanobis distance between zj (five)) is calculated as follows. ~ λ ~ ^ Μ ) ^ ^ zJr~1zx (59) can get 32 - ^ (60) 201212140 . The G-edge value of the J-th order process data is now. After obtaining the (10) value, the (10) gate root value (which) should be defined. Generally, the -= G57 threshold is 2 to 3 times the maximum value of the historical process parameter data (where "representing the parent one, and the historical process parameter data"). Referring to Figure 5, the scale (4) of the present invention - implementation For example, in the process control (APC) method, step 200 is performed to obtain the complex array history process parameter data, wherein this = historical process parameter, the shell material system is a process machine The stage is used to process the plurality of solid soil history workpieces. Step 21 is performed to obtain the historical workpieces being measured by a measuring machine. The plurality of historical measuring materials are measured, wherein the historical measuring data is respectively according to step 200. The historical workpieces produced by the historical process parameter data correspond to the measured actual measured values one by one. Step 22 is performed to use the historical process parameter data and the historical measurement values corresponding to the historical process parameter data one by one and according to The estimation algorithm is used to establish a prediction model; the historical process parameter data and the historical measurement value corresponding to the historical process parameter data are used to establish a reference model by reference to the algorithm; The distance algorithm is used and the historical process parameter data is used to establish a statistical distance model. Step 230 is performed to enable the R2R controller to control the aforementioned process machine to perform the process batch according to the aforementioned equations (13) to (15). The above embodiments may be implemented by a computer program product, which may include a machine readable medium having a plurality of deductions, and the instructions may be programmed to perform the steps in the above embodiments. Read 33 201212140=Body is not limited to floppy disk, read-only memory, random access memory 7 &gt; handle, magneto-optical disk, (EPROM), electronic erasable two erasable programmable read-only memory card _Cal card) or magnetic card; the machine of the recording and optical command can be Wei (4) \ body or any suitable for storing electronic computer program products to download, Α The embodiment shown in this example can also be used as a connection such as a line) The connection (for example, the network connection - from the remote computer to the requesting computer. The female exemplified example to illustrate the embodiments of the present invention is useful and advantageous. Regular maintenance (Periodi c Maintenance; PM) The TM control of the cycle (10) machine is an illustrative example for evaluation and comparison. The simulation conditions and plots are listed below. 1./ “The actual removal of the film thickness measured by the measurement machine And the actual film thickness of the wafer after the A batch is executed by the household CMP machine. /W, the specification is fine ±15G angstrom (A), and its towel surface is the target value, called . Thus: P〇stYk = PreYk~yk (61) yk ~ ARRk * (62) where J is the actual removal rate of the second batch, and is called the grinding time in this example. The famous Preston equation is proposed here to predict the CMP removal rate. This Preston equation was discovered by the 1927 glass polishing time experiment. According to the Preston equation, the material removal rate is affected by the following factors: the fixed pressure at the contact point (also known as the machine pressure); the relative velocity of the contact point between the circle and the polishing pad at 201212140 (also known as the machine). Table speed); a constant representing the effect of the remaining parameters, including the slurry fluid velocity, the polishing pad properties, and the like. It is thus simulated by the following equation: , =(4x(^^M^^)x(^^))+_+m2) + — (63)

Stress 1, Stress 2, Rotspdl, R〇tspd 2, Sfuspdl, Sfuspd 2, PM1, PM 2 and five mW series are shown in Table 2. The Nominal removal rate of equation (63) is modeled by a polynomial curve fit of the number of parts used by the regular maintenance room (referred to as PU varying from 1 to 600). 4t=(4xl0&quot;6)x(/&gt;t/-l)3-(3.4x10_3)x(Pt/-l)2+(6.9xl0~3)x(/&gt;C/-1)+( 1.202xl03) (64) 2. Represents the predicted value of the lamp on the corpse, then, by equations (61) and (62), yk = ARRk*uk (65)

PostYk = PreYk -yk= PreYk - ARRk * uk (66) where ARRk = /(Stress, Rotspd, Sfuspd, PU,PU2,PUy) (67) ^The virtual measurement (VM) value of the brother-in-law, which has Process parameters and (= Stress 1+Stress2), Rotspd {^Rotspdl+Rotspd2), Sfuspd l=Sfuspdl+Sfuspd2), PU, PU2, PU3. The two Stress, Rotspd, Sfuspd, Ft/, corpse t/, and Pt/ process parameters are based on the Preston equation, equations (63) and (64). The set value series of the simulated process parameters are shown in Table 35 201212140 Table 2 Simulation - Parameter definition and set value Abbreviation Definition Setting value Average variation Error White noise represents random error 0 300 PM1 Variation of machine parts caused by regular maintenance Error caused by 0 100 PM2 Machine part variation random error 0 6 Stress 1 Machine pressure error caused by reassembly during regular maintenance 1000 2000 Stress2 Random disturbance of machine pressure 0 20 Rotspdl Machine due to reassembly during regular maintenance Speed error 100 25 Rotspd2 Random disturbance of machine speed 0 1.2 Sfuspdl Slurry fluid velocity error due to reassembly during regular maintenance 100 25 Sfuspd2 Random disturbance of slurry fluid velocity 0 1.2 PreYk Effect A: Batch process results Pre-treatment (etching depth) value of 3800 2500 3. The control action of the k+th batch is derived from

Tgtk+l = P^Yk+l -Tgtp〇stY Sand “1 – 4+1 Λ +1 4. When measuring with a physical measuring machine, when PiwiA is estimated with a virtual measurement module , ^Λ+1 = «2,* (λ - ) + (! - «2.Α )vk where (68)(69) (70) 36 (71) 201212140 a2^f(RIk, GSIk)xa] (72)

^ r 〇, if RIk&lt;RITor GSIk &gt; GSIT ^ where f(Rlk, GSIk) = 4 T^hiiRJk&gt;RITandGSIk&lt;GSITmdiork&lt;C (73)

1 -/?/, . if RJ, &gt; RJ^ and GSJ, &lt; GSJ^ and for k &gt; C In this example, 025. 5. 1 lot (Lot) = 25 pieces, the second part is the sampled part. 6. CpA: represents the process capability, and its equation is as follows:

Cpk (Process Capabilit)·) = niin UCL-mean(PostY) mean{PostYyLCL 3'Kstd{PostY) ' 3xstd{PostY) (74) where ί/CZ = 2950 and LCX = 2650.

ΣI (PostYi - TgtP0StY) / TgtP0SlY I 7* MAPE Process =~-_k-&gt;&lt;brain (75) 8. On samples 5〇, in, 179, 251, 349 and 503, also added by the mean (Mean) = 0 and additional random perturbations caused by S/wpW of Variance = 0.36. In other words, the combined variation of milk/2 in samples 50, 111, 179, 251, 349, and 503 was 1.2 + 〇·36 = 1.56. When these additional random perturbations are present, the corresponding j?/ and / or GS/ values may exceed their threshold values. Five rounds of simulations with different random seeds were performed to evaluate and compare performance. For each round, the simulation results of PreA, Γ, and _ of women = 1 to 600 are generated based on the set values of Table 2 and equations (68), (64), and (63), respectively. Then, set %=0·35 and eat=0 to calculate 吣, and apply equations (62), (70), (69), and (61) to calculate five cases respectively. 2 out of 5 4+1, called +; and corpse. As for =3 ~ _, the control mechanisms of the five cases are different and are described below.

Case 1: Let R2R of Insitu be set to 0=〇.35, and use equations (62), (7〇), (69), and (61) to calculate no =3~600 respectively. Righteousness, _ and household (10) heart. Slaughter 2: R2R+VM without and / (α2 = α, = 0.35, and using equations (65), (71), (69), (66) and (61) to calculate separately Exit = 3~600 of H, %+/, / and PostYk °

Rate Example 3: R2R+VM with /?/ is set to %= 0.35. If or GS7>GS7r, set ==〇; No

Then set α2, *= private call. Apply equations (65), (71), (69), (66), and (61) to calculate moxibustion = 3 to 600, +1, z/correction, corpse (10) ή, and />; . y Example 4: 柹 (1- R2R+VM of the brother-in-law sets % = 0.35. If /?/ &lt; or C?57 &gt; GSTj·, then set α2 = 〇; otherwise set ^=(1 a private) ΧΑ Apply Equations (65), (71), (69), (66), and (61) to calculate A = 3 to 600, 4+1, +7, p(10)$, and PostYk, respectively.

Case s: R2R+VM for Nanxun//Π Set %= 0.35. Apply a similar/(1-like) switching mechanism as shown in equations (72) and (73) to set A; and apply equations (65), (71), (69), (66), and (61) to respectively Calculate moxibustion = 3 to 600, &amp; +1, w correction, and

PostYk ° applies cPk (process capability index) and MAPEPr as shown in equations (74) and (75), respectively. (10) (Mean Absolute Percentage Error; relative to the process 38 201212140 average absolute error of the target value) to evaluate and compare the performance of these five cases. The Cpk value and the MAPEP_S value of the five cases are shown in Tables 3 and 4, respectively. Observing Tables 3 and 4 and comparing Case 1 with the baseline, it is clear that Case 2 (which was not used and //GS/) performed the worst. Case 3 (which uses and //GS/ filters out bad quality iUVM) values and sets α2 = /?/χαι) is the most natural method and has acceptable performance. Except for Round 1, Case 4 (which uses and/or still/filters out poor quality corpse 0·^ (VM) values and sets α2 = (1 -like) X %) performs better than Case 3. Case 5 (which uses the P(10)^(VM) value that filters out bad quality and uses the switching mechanism of equation (73)) to fix the problem of case 4 in round 1; the performance of case 5 is equivalent to case 1 (using actual field measurement) Consistent. Table 3 Cpk value rounds for five APC method cases Ψ In 1: In situ Case 2: VM Things 3: VM+RI ¢#14: VM+ fl-RI) Example 5: VM+RI/il-Rll 1- 25 1 ~ 200 1-600 1-25 1-200 1 ~ 600 1-25 1-200 卜 600 卜 25 1-200 1-600 1~25 1~200 1-600 —1 1.09 1.58 1.62 1.14 1.42 1.31 1.14 1.54 1.49 1.12 1.29 1.38 1.14 1.57 1.55 2 1.73 1.89 1.86 1.51 1.64 1.72 1.51 1.73 1.77 1.89 2.00 2.04 1.51 1.71 1.74 3 1.60 1.74 1.77 1.72 1.64 1.77 1.72 1.72 1.80 1.76 1.79 1.87 1.72 1.85 1.90 4 1.43 1.95 1.87 1.45 1.74 1.72 1.45 1.89 1.76 1.51 1.95 1.87 1.45 1.94 1.87 5 1.32 1.85 1.81 1.41 1.78 1.71 1.41 1.83 1.79 1.33 1.77 1.81 1.41 1.89 1.86 1.7 Average 1.43 1.80 1.80 1.45 1.64 1.65 1.45 1.74 1.72 1.52 1.76 1.80 1.45 L79 1.78 Table 4 MAPEPlOcess value round of 5 APC method examples Case 1: Insitu Case 2: VM Case 3: VM+RI Case 4: VM+(1-RI&gt; Case S: VM+RI/(1-RI) 1~25 1-200 1-600 1~25 Bu 200 1400 N25 1-200 1-600 Bu 25 Bu 200 1-600 1-25 1 ~200 1^600 -J 1.13% 0.86% 0.86% 1.35% 1.00% 1.07% 1.35% 0.94% 1.00% 2.52% 1.45% 1.15% 1.35% 0.98% 0.97% 2 0.85% 0.75% 0.76% 0.98% 0.87% 0.81% 0.97% 0.84% 0.79% 0.80% 0.72% 0.69% 0.97% 1.05% 0.82% 3 0.84% 0.85% 0.82% 0.94% 0.86% 0.81% 0.94% 0.83% 0.79% 1.03% 0.80% 0.76% 0 94% 0.77% 0.75% 4 0.93% 0.73% 0.76% 1.11% 0.83% 0.83% 1.11% 0.78% 0.82% 1.07% 0.84% 0.79% 1.11% 0.84% 0.79% 5 0.99% 0.75% 0.78% 1.05% 0.78% 0.82% 1.05% 0.77% 0.80% 1.41% 0.83% 0.78% 1.05% 0.77% 0.76% Average 0.95 % 0.79% 0.80% 1.08% 0.87% 0.87% 1.09% 0.83% 0.84% 1.37% 0.93% 0.83% 1.09% 0.88% 0.82% The simulation results of the rounds 1 of the five cases are shown in Fig. 6A to Fig. 6E, Fig. 39201212140, in which the first 400 workpieces are shown. Since additional random perturbations caused by * having a mean value (Mean) = 0 and a variation value (Variance) = 0.36 are added to the samples 50, 111, 179, 251, 349, and 503, poor quality is generated. Values are plotted as shown in Figure 6B. These bad VM values as shown in Figure 6B can be detected by &/or GS/. In this example, the setting and GiS/t1 are respectively 0.7 and 9. The case of the sample 50 of the round 1 and the case of GS/&gt;GS/r; and the case of the GS/&gt;G*S7r of the sample of the round 1 are enlarged and shown in Figs. 7 and 8. As shown in Fig. 7, the (VM) value of the various cases of the sample 50 is deviated by the additional variation value of 0.36 added to S/ks/^2. Since </^ and GS/&gt;GS7r' filter the P(10)4 values of cases 3, 4, and 5 by setting %=〇', the household (four) value of case 2 is still used as α2 = αι=〇35 To adjust the R2R controller gain. The effect of filtering the bad quality of the households on the 匕 value is shown in the sample 51, which shows that the value of the case 2 is pulled down by the controller because the value of the sample is still too high. As for other cases, the values of and are not much different. As can be seen from the observation of Fig. 8, the values of the various cases of the sample 349 are deviated from the additional variation value 〇.36 added to the 5/7 heart. In this case, only OS7 exceeds its threshold. Similarly, the values of the bad qualities of Cases 3, 4, and 5 are discarded, but the value of the bad quality of Case 2 is not discarded. Therefore, as shown in Figure 8, the R2R control generated by Case 2 due to improper use of the value will result in a sudden high 201212140. The evidence shown in Figures 7 and 8 shows that the result of using the unworthy VM value is worse than the case of not using the VM at all. ° As mentioned earlier, when away from the target value or the production process is relatively unstable, set %=Λ/χαι. Conversely, if PosiA is close to the target value or the production process is relatively stable, then it is set. The present invention has been disclosed in the above embodiments, and is not intended to limit the invention to any of the ordinary skill in the art without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention is defined by the scope of the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS In order to make the above and other objects, features, advantages and embodiments of the present invention more obvious, the description of the drawings is as follows: Figure 1 shows an exponentially weighted moving average (EWMA) A block diagram of a conventional model of R2R control. Figure 2 is a block diagram showing the conventional W2W control mechanism using virtual measurement.

Figure 3A is a schematic diagram showing a W2W APC system in accordance with an embodiment of the present invention. Figure 3B is a schematic diagram of an EWMA controller in accordance with an embodiment of the present invention. Figure 4A is a schematic diagram showing the confidence index values defined for use in embodiments of the present invention. FIG. 4B is a schematic diagram showing the definition of the confidence indicator gate 201212140 in accordance with an embodiment of the present invention. Figure 5 is a flow chart showing the flow of the W2W APC method in accordance with an embodiment of the present invention. Figures 6A through 6E show the simulation results of the first 400 workpieces in five cases. Figure 7 shows the simulation results for the 45th to 55th workpieces in 5 cases. Figure 8 shows the simulation results of the 344th to 354th workpieces in 5 cases. Process machine virtual measurement module overall similarity index module [main component symbol description 10: process machine 30: virtual measurement module 100 120 124 20: measurement machine 40: R2R controller 110: measuring machine Station 122: Confidence Index Module 130: R2R Controller 2 00 Acquires Complex Array History Process Parameter Data 210 Acquires Multiple Historical Measurement Data 220 Establishes Estimation Model, Reference Model, and Statistical Distance Model 230 to enable the R2R controller to control the process machine Taiwan to process batches 42

Claims (1)

201212140 VII. Patent application scope: 1. An Advanced Process Control (APC) system, comprising: a processing machine for processing a plurality of historical workpieces according to the complex array historical process parameter data, and according to The multi-array process parameter data is used to perform a plurality of process batches (Run) on a plurality of workpieces; a measuring machine platform for measuring the historical workpieces and a plurality of sampled workpieces selected from the historical workpieces to provide the plurality of sampled workpieces a plurality of historical measurement data of the historical artifacts, and a plurality of actual measured values of the sampled workpieces that have been processed in the process batches; a virtual metrology (VM) module for borrowing Entering a set of process parameter data into an estimation model to provide a plurality of virtual measurements of the process batches, wherein the estimation model is established according to a second estimation algorithm and using the group history Process parameter data and the historical and measured values, wherein the historical measured values are respectively corresponding to the historical ones of the historical manufacturing process Actual measurement value; - Confidence refers to the reduction group's number of letters used to generate the recordings:: Rdianee Index, corresponding to each of the process batches, the value of the heart index is calculated by The statistical distribution of the virtual measurement value of the piece 3 == srutiQn) and the statistical calculation of the workpiece-reference value are input to the process parameter data of the workpiece; = value: f Λ 'Course parameter data and with the group history ^^^ These, historical system J history measurement value, the estimated performance; 43 201212140 When the overlap area is larger, the higher the confidence index value, the higher the credibility of the virtual measurement value representing the confidence index value; And _2 times to batch (Run as Run; R2R) controller, used to control the process machine according to the following relationship to carry out the process batch: "Z+1 = g (G丨丨, Gl2,... , GM, less J; ~+i=g(G2i, G22,&quot;.,G2,.,j)J; G2j = f(RJk)xGu ; where if the inverse ^ &lt; , the next to the batch controller G2/=0 'or adjust the batch to PRITlk instead of λ. C kRIT JLk> where A represents the actual measured value; then /(called)=^ ; then /(/3⁄4) = 1 — from; Z system The sampled workpiece processed in the batch ~ represents the 2+th; the control action of the secondary process batch; the (four) ^ time helps the batch to the batch controller ^ &quot;: Gam) 'where z• represents the number of controller gains applied to the batch to batch controller; K measured value^ represents the virtual amount of the workpiece that has been processed in the U-process batch, as represented by The control action of the second owe process batch; the control: the value of the confidence indicator applied to the batch to the batch controller in the batch to the batch controller when the λ is used; - the maximum allowable error upper limit -w threshold value 44 201212140 The maximum allowable error upper limit is defined by the error of the virtual-measurement value obtained from the estimation model; and • c represents a preset process batch The number of times. 2. The advanced process control system of claim 1, wherein the reference algorithm and the estimation algorithm are respectively selected from a multi-regression (MR) algorithm and a support vector machine Support-Vector-Regression SVR) algorithm, Neural-Networks (NN) algorithm, Partial-Least-Squares Regression (PLSR) algorithm and Gaussian-process-regression (GPR) algorithm One of the groups that make up. 3. The advanced process control system of claim 1, further comprising: an overall similarity indicator module for providing the process batches by inputting the set of process parameter data to a statistical distance model The plurality of global similarity index values (OT/), the statistical distance model is established according to a statistical distance algorithm and uses the set of historical process parameter data, wherein if 63⁄4 &gt; (73⁄4' then 2 calving, or using IX instead of A to adjust the batch to batch controller, where GiS7;t represents the overall similarity indicator value of the kth process batch; represents the threshold based on a G, the G57 The threshold value is defined as the maximum overall similarity of the historical process parameter data of the group is 2 to 3 times the value of the ladder. 4. The advanced process control system as described in claim 3, wherein the statistics 45 201212140 distance algorithm is one Mahalanobis Distance algorithm or Euclidean Distance algorithm. 5. Advanced process control system as described in claim 1, wherein the batch to batch controller is one Moving Average (ΜA) controller, Exponentially Weighted Moving Average (EWMA) controller, a double exponentially weighted moving average (Double EWMA) controller, or a proportional-integral-derivative (Proportional- Integral-Derivative; PID) controller 6. An advanced process control method, including: obtaining complex array history process parameter data 'These sets of historical process loss data are used by a process machine to process a plurality of historical artifacts; Obtaining a plurality of historical measurement data measured by a measuring machine of the historical workpieces, wherein the historical workpieces are respectively manufactured according to the historical data of the group of processes; &gt; using the historical parameter data of the group and And the historical measurement values corresponding to the historical process parameter data of the group, the estimation model is established according to a estimation algorithm, and a reference model is established according to a reference algorithm, and the estimation is adopted. The algorithm and the reference algorithm must be no, algorithm; , ., ,, and the same to make a batch to batch controller root The following relationship controls the process machine to process the batch: &quot;&quot; 46 201212140 M*+ig(G21,G22,; G2j= f(RIk)xGul; where if private &quot;, then G2r〇, or Use L instead of λ to adjust the batch to the batch controller; right edge kkRITM^ kSC, then f(RIk)=:Ji/k ·, if and bC then / (call)=1-Hong; Represents an actual measured value of the workpiece that has been processed by the processing machine and sampled by the measuring machine in the z-th process batch; ～1 represents the first when the 氕 is used: +/min The control action of the batch; G u represents the control H gain (Gain) applied to the batch to batch controller in just the time, the towel/wire should be in the batch: owed to the batch controller The number of controller gains; λ represents a virtual measurement of a workpiece that has been processed by the processing machine in the &amp; process batch, the virtual measurement being processed by one of the workpieces The parameter data is generated by the estimation model; the Η represents the control action when the zero-time no +/-process batch is adopted; The batch-to-batch controller gain; Μ and Α represent a confidence indicator value for the first process batch, wherein the confidence indicator value corresponding to the A-human process batch is calculated by calculating the workpiece; The statistical distribution of the virtual measured value and the statistical value of the reference predicted value of the workpiece are generated by an overlapping area, wherein the reference prediction of the workpiece is: by inputting the set of process parameter data of the workpiece to the The reference model is generated, wherein the larger the overlap area is, the higher the confidence index value is, the representative of the 201212140 table corresponds to the virtual measure value of the confidence indicator value of the gentleman product. And h represents based on a maximum The upper limit of the allowable error - the upper limit of the maximum allowable error is defined by the error of the measured value from the estimated model; and ^ is a predetermined process batch Number of times 7. According to the advanced process control method described in claim 6, the reference algorithm and the estimation algorithm are respectively selected from a multi-regression (MR) algorithm and a support vector machine support. -Vector-Regress SVR) algorithm, Neural-Networks (NN) algorithm, Partial-Least-Squares Regression (PLSR) algorithm and Gaussian-process-regression (GPR) calculus A group of people formed by law. 8. The advanced process control method according to claim 6, further comprising: establishing a statistical distance model according to a statistical distance algorithm and using the set of historical process parameter materials; &gt; making the batch to batch controller The process can be controlled according to the following relationship: If, then, G2, calving, or using nine instead of nine to adjust the batch to the batch control, the representative of the towel is: The first one = body similarity index value 'the overall similarity index value is generated by inputting the set of process parameter data to the statistical distance model; which represents the arc threshold, and the (10) gate weight is defined as These 48 201212140 group historical process parameter data are 2 to 3 times the maximum overall similarity index value. 9. The advanced process control method of claim 8, wherein the statistical distance decision algorithm is a Mahaian 〇 Distance algorithm or an Euclidean Distance algorithm. 10. The advanced process control method according to claim 6, wherein the batch to the batch controller is a moving average (MA) controller, an exponential force σ weight moving average (EWMA) controller, a double index A weighted moving average controller, or a proportional-integral-derivative (pID) controller. Product &amp; Advanced System ’ When the computer is loaded into this computer to any of the 11. Computer Program Products and executed, the method of request control can be completed. 49